Lemma 2.2 [1]}
Let \(a, b \in  {\mathbb {F}}_{2^n}\)  and \(a \ne 0\) . Then the quadratic equation \(x^2+ax+b=0\)  has solutions in \( {\mathbb {F}}_{2^n}\)  if and only if \({\rm Tr}_{n}(\frac{b}{a^2})=0\) .

